Question

先化简 再求值.((a平方-2ab+b平方)/(a平方-b平方))/(1/a-1/b)其中a=根号3+1b＝根号3-1

Answer 1

.((a平方-2ab+b平方)/(a平方-b平方))/(1/a-1/b)
={(a-b)^2/[(a-b)(a+b)]}/[(b-a)/ab]
=[(a-b)/(a+b)]*ab/(b-a)
=-ab/(a+b)
=-2/2√3
=-√3/3

Answer 2

a=根号3+1b＝根号3-1
∴a+b=2√ 3
av=3-1=2

.((a平方-2ab+b平方)/(a平方-b平方))/(1/a-1/b)
=(a+b)(a-b)/(a-b)²×(b-a)/ab
=-(a+b)/ab
=-2√ 3/2
=- √3

Answer 3

化简是（-ab）/(a+b)，由a=根号3+1b＝根号3-1 ，知a=根号3-1,b=(根号3-1)/(根号3+1)=2-根号3，所以最后结果为5-3根号3